Question

How do you solve the following system?: `-1/2x+5y=-20 , 3x-2y=1`

Answer 1

`x=-105/42` and `y=-119/28`

Explanation:

The given system
`-1/2x+5y=-20` and `3x-2y=1`

Let us use the method of substitution

From the second equation `3x-2y=1`

`x=(1+2y)/3`

We use the second in the first equation

`-1/2x+5y=-20`

`-1/2((1+2y)/3)+5y=-20`

`-((1+2y)/3)+10y=-40`

`((1+2y)/3)-10y=40`

`1+2y-30y=120`

`-28y=119`

`y=-119/28`
~~~~~~~~~~~~~~~~~~~~~~~

Solve for `x`

`x=(1+2(-119/28))/3`

`x=(28-238)/84`

`x=-210/84`

`x=-105/42`
~~~~~~~~~~~~~~~~~~~~~~

Checking:at `x=-105/42` and `y=-119/28`

`-1/2x+5y=-20`
`-1/2(-105/42)+5(-119/28)=-20`

`105/84-595/28=-20`

`(105-1785)/84=-20`

`(-1680)/84=-20`

#-20=-20

Also

`3x-2y=1`

`3(-105/42)-2(-119/28)=1`

`-105/14+119/14=1`

`14/14=1`

`1=1`

Correct ! at `x=-105/42` and `y=-119/28`

God bless....I hope the explanation is useful.